Hi Lukin,
Firstly, sorry to hear your website got hit. You aren't the first and certainly not the last! The first thing to do in order to try and recover is to be completely honest with the links that were built. If you had an external agency build links then ask them for a full report (you should already have this but not all agencies do this as standard) on what has been done. This will allow you to understand the kinds of links that have been built.
In my opinion, no tool out there is good enough and whatever info they give you, you have to check it anyway. The process to recovery is a long one because the only way is to manually look at every link to your website and analyse whether Google thinks it is spammy or not. Depending on the size of your link profile, this may be considerably time consuming but, unfortunately, it has to be done.
We have managed to recover websites and whilst we used to try and get them manually deleted first then disavow, we have managed to recover websites without deleting a single link. Google WILL NOT open any external documents that are sent to them so sending them stuff probably won't help much. We are very stringent with the links we disavow and sometimes there will be links that you can't even find that are holding you back, however, Google should tell you the types of links that are harming you and you can look deeper into them.
I'd say use as many tools as you can to see as many links to your website as possible, so use WMT and OSE and any others you might have access to. Once you have a complete list of links, ask yourself "Would I show my profile to Matt Cutts?"
It can be a long process (from 4-6 weeks to 6-12 months) but if your website is worth keeping then it is worth the time and effort spent.
All the best,
Karl